Graphing the Logarithmic Parent Function
Description/Explanation/Highlights
Video Description
This video explains how to graph the logarithmic parent function by using the inverse of the exponential function.
Steps and Key Points to Remember
To graph a logarithmic parent function using the inverse, follow these steps:
- Logarithms have multiple parent functions with each base having its own. For example \(y=\log_2x\) is the parent function for a base 2 log.
- Recall that the logarithmic function is the inverse of an exponential function, so if we rewrite the log in exponential form we get \(2^y=x\) and when we switch x and y, we will have the inverse of the base 2 parent. \(2^x=y\)
- If we make a table of values such as (-2, .25) (-1, .5) (0, 1) (1, 2) (2, 4) found by picking values of x and plugging them into the equation to find y, we could use it to graph the exponential function.
- Recall that to graph inverses, we switch the x and y values in the table. If we were to do that with exponential table giving us (.25, -2) (.5, -1) (1, 0) (2, 1) (4, 2) we would have points that are on the inverse function, which would be the logarithmic function!
- Graph these points and connect them with a smooth curve and you will have graphed the log parent.
- It is usually easier after rewriting in exponent form to simply pick the y-values first and then plug them in to find x instead of switching x and y and then switching back. The result is the same.
Here are some key points to keep in mind when using the inverse to graph a logarithmic parent function.
- Logarithmic functions have multiple parents; one for each base.
- Log functions and exponential functions are inverses of each other.
- Finding inverses of graphs is as simple as switching the x- and y-values and graphing the new coordinates.
- Rewriting from log to exponential and switching x and y finds the inverse of the log.
- Switching the x and y values in a table of the exponential form takes us back to a log.
- Finding the inverse and switching x and y values back works to graph a parent log of any base.
Video Highlights
- 00:00 Introduction
- 00:33 Single example of graphing the parent function of a base 2 log
- To watch this video on YouTube in a new window with clickable highlights, click here
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